Stream ciphers use the output of a Pseudo-Random (PR) generator to mask the information stream. The security of these cipher systems ultimately depends on the structure of the PR generator. There are some minimum necessary criteria such as long period, flat statistical distribution and high linear complexity that the PR generator of a stream cipher system should satisfy to resist the basic cryptanalytic attacks on such systems. We propose a class of PR generators using the coset elements of a Reed-Muller code. The linear Complexity of these generators is analysed and conditions that assure the highest possible linear complexity for them are specified. It is shown that the above mentioned criteria do not gurantee the security of a stream cipher system and the proposed PR generator, although it satisfies all of them, is not secure.